Inexact Bayesian point pattern matching for linear transformations

• We model matching sets of points related by linear transformations.
• We model inexact matching (not a complete 1-1 correspondence) of noisy points.
• Variational Bayesian methods give computationally efficient posteriors for variables.
• Posterior matching probabilities indicate matched and unmatched points between sets.
• Technique is demonstrated on 3D synthetic data and optical microscopy image stacks.

We introduce a novel Bayesian inexact point pattern matching model that assumes that a linear transformation relates the two sets of points. The matching problem is inexact due to the lack of one-to-one correspondence between the point sets and the presence of noise. The algorithm is itself inexact; we use variational Bayesian approximation to estimate the posterior distributions in the face of a problematic evidence term. The method turns out to be similar in structure to the iterative closest point algorithm.